1 ReadMe

This is the analysis for study 3 of the MBC project, alias the counterfactual study.
The study had N = 50 (before exclusions), and subjects saw two conditions: Intervention and Similarity, with 15 trials per condition.

2 Set options

knitr::opts_chunk$set(echo = TRUE)

library(pacman)
pacman::p_load(
               lme4, 
               lmerTest,
               here, 
               patchwork, 
               cowplot, 
               viridis, 
               effects, 
               conflicted,
               gt,
               webshot2,
               knitr,
               performance,
               tidyverse,
               simr)

walk(c("select", "filter", "rename", "mutate", "summarise", "summarize"), ~ conflict_prefer(.x, "dplyr"))
## [conflicted] Will prefer dplyr::select over any other package.
## [conflicted] Will prefer dplyr::filter over any other package.
## [conflicted] Will prefer dplyr::rename over any other package.
## [conflicted] Will prefer dplyr::mutate over any other package.
## [conflicted] Will prefer dplyr::summarise over any other package.
## [conflicted] Will prefer dplyr::summarize over any other package.
conflicts_prefer(simr::fixed)
## [conflicted] Will prefer simr::fixed over any other package.
sessionInfo()
## R version 4.4.0 (2024-04-24)
## Platform: aarch64-apple-darwin20
## Running under: macOS 15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: America/New_York
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] simr_1.0.7         lubridate_1.9.3    forcats_1.0.0      stringr_1.5.1     
##  [5] dplyr_1.1.4        purrr_1.0.2        readr_2.1.5        tidyr_1.3.1       
##  [9] tibble_3.2.1       ggplot2_3.5.1      tidyverse_2.0.0    performance_0.13.0
## [13] knitr_1.46         webshot2_0.1.1     gt_0.11.1          conflicted_1.2.0  
## [17] effects_4.2-2      carData_3.0-5      viridis_0.6.5      viridisLite_0.4.2 
## [21] cowplot_1.1.3      patchwork_1.2.0    here_1.0.1         lmerTest_3.1-3    
## [25] lme4_1.1-35.4      Matrix_1.7-2       pacman_0.5.1      
## 
## loaded via a namespace (and not attached):
##  [1] tidyselect_1.2.1    RLRsim_3.1-8        fastmap_1.1.1      
##  [4] promises_1.3.0      digest_0.6.35       timechange_0.3.0   
##  [7] lifecycle_1.0.4     survival_3.5-8      processx_3.8.4     
## [10] magrittr_2.0.3      compiler_4.4.0      rlang_1.1.5        
## [13] sass_0.4.9          tools_4.4.0         plotrix_3.8-4      
## [16] utf8_1.2.4          yaml_2.3.8          plyr_1.8.9         
## [19] xml2_1.3.6          abind_1.4-5         websocket_1.4.2    
## [22] withr_3.0.0         numDeriv_2016.8-1.1 nnet_7.3-19        
## [25] grid_4.4.0          fansi_1.0.6         colorspace_2.1-0   
## [28] iterators_1.0.14    scales_1.3.0        MASS_7.3-60.2      
## [31] insight_1.2.0       cli_3.6.4           survey_4.4-2       
## [34] rmarkdown_2.29      generics_0.1.3      binom_1.1-1.1      
## [37] rstudioapi_0.16.0   tzdb_0.4.0          minqa_1.2.7        
## [40] DBI_1.2.2           cachem_1.0.8        chromote_0.4.0     
## [43] splines_4.4.0       parallel_4.4.0      mitools_2.4        
## [46] vctrs_0.6.5         boot_1.3-30         jsonlite_1.8.8     
## [49] car_3.1-2           bookdown_0.39       hms_1.1.3          
## [52] pbkrtest_0.5.3      jquerylib_0.1.4     glue_1.8.0         
## [55] nloptr_2.1.1        ps_1.7.6            stringi_1.8.3      
## [58] gtable_0.3.5        later_1.3.2         munsell_0.5.1      
## [61] pillar_1.9.0        htmltools_0.5.8.1   R6_2.5.1           
## [64] rprojroot_2.0.4     evaluate_0.23       lattice_0.22-6     
## [67] backports_1.4.1     broom_1.0.5         memoise_2.0.1      
## [70] bslib_0.7.0         Rcpp_1.0.12         gridExtra_2.3      
## [73] nlme_3.1-164        mgcv_1.9-1          xfun_0.43          
## [76] pkgconfig_2.0.3

3 Global variables

base_path <- here("code", "pilot")
freesort_and_causal_distances_df_path <- paste0(base_path,
                                                "/data/data-study4-explanations/freesort_minus_causals.csv")
#nb: distances are in study 4 explanations, just keep in mind

4 Study 3 - Counterfactuals

4.1 Prepare data

4.1.1 read data

data_path_cf <- paste0(base_path, "/data/data-study3-counterfactuals/pilot3")

desired_order <- c("see something", "hear something", "choose what to do", 
                   "remember something", "think about something", "reach for something", 
                   "sit down", "jump up and down", "kick something", "take a walk", 
                   "get tired", "become hungry", "feel scared", "experience pain", "get sick")

file_paths <- list.files(path = data_path_cf, pattern = "^2025-", full.names = TRUE)

d <- imap_dfr(file_paths, ~ {
  read_csv(.x, col_types = cols(response = col_character())) %>%
    mutate(
      filename = basename(.x),
      subject_id = paste0("subj_", str_pad(.y, 2, pad = "0"))
    )}) %>%
  select(-c(mturk_participant_id, mturk_assignment_id, mturk_project_id)) %>%
  relocate(subject_id, .before = "success")

4.1.2 demographics

# demographics
df_demographics <- d %>% 
  filter(trial_id == "demographics_survey") %>% 
  select("trial_id", "filename", 
         "feedback", "age", "ethnicity", "gender", "race") 

summary(df_demographics$age)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   20.00   29.00   35.50   38.06   45.00   70.00
table(df_demographics$gender)
## 
##     Female       Male Non-binary 
##         21         28          1
table(df_demographics$ethnicity)
## 
##     Hispanic Non-Hispanic 
##            2           48
table(df_demographics$race)
## 
## American Indian/Alaska Native                         Asian 
##                             1                             9 
##        Black/African American                         White 
##                             6                            33 
##         White and South Asian 
##                             1

4.1.3 wrangle data

initial: 30 trials * 48 subjects = 1440 rows. dat: (30 trials / 2 trials per row) * 48 subjects = 720 rows.

TODO: rename itemB to target item.

subjects_to_exclude <- d %>%
  filter(grepl("attention_check", condition)) %>% 
  filter(attn_correct == "no") %>% 
  pull(subject_id) %>% 
  unique()

dat <- d %>% 
  filter(!subject_id %in% subjects_to_exclude) %>%
  filter(condition %in% c("counterfactual", "similarity")) %>% 
  mutate(condition = ifelse(condition == "counterfactual", "causal", condition)) %>% #meant to call it causal (both are counterfactuals)
  mutate(response = as.factor(response)) %>% 
  mutate(condition = as.factor(condition)) %>% 
  select(-condition) %>% 
  select(subject_id, itemB, causal_itemA, similar_itemA, response_value) %>% 
  mutate(causal_itemA = factor(causal_itemA, levels = desired_order), #this col has unique values; we're assigning 15 lvls
         similar_itemA = factor(similar_itemA, levels = desired_order), #this col has unique values; we're assigning 15 lvls
         itemB = factor(itemB, levels = desired_order)) %>% 
  # filter(subject_id == "subj_01" & itemB == "see something") %>% 
  mutate(item_type = case_when(
        !is.na(causal_itemA) ~ "causal_itemA",
        !is.na(similar_itemA) ~ "similar_itemA"),
        item = coalesce(as.character(causal_itemA), as.character(similar_itemA))) %>% 
  select(-causal_itemA, -similar_itemA) %>% 
  pivot_wider(names_from = item_type,
              values_from = c(item, response_value)) %>% 
  rename("causal_itemA" = item_causal_itemA,
         "similar_itemA" = item_similar_itemA, 
         "causal_itemA_counterfactual" = response_value_causal_itemA,
         "similar_itemA_counterfactual" = response_value_similar_itemA) 

4.2 plot dv vs conditions

4.2.1 prepare to plot

dat_plot <- dat %>% 
  rename("causal" = causal_itemA_counterfactual,
         "similar" = similar_itemA_counterfactual) %>% 
  pivot_longer(cols = c("causal", "similar"), 
               names_to = "counterfactual_type",
               values_to = "likelihood") 

4.2.2 plot dv vs counterfactual type

figure for spp poster

main_fig <- 
dat_plot %>% 
  mutate(counterfactual_type = factor(counterfactual_type, levels = c("similar", "causal"))) %>% 
  ggplot(aes(x = counterfactual_type, y = likelihood, fill = counterfactual_type)) +
  stat_summary(fun.data = mean_se, geom = "bar", color = "black") +
  stat_summary(fun.data = mean_se, geom = "errorbar", width = .2) +
  geom_hline(yintercept = 50, linetype = "dashed") +
  labs(y = "Likelihood of Counterfactual", 
       x = "Preceding Item Type",
       fill = "Preceding Item Type") +
  scale_x_discrete(labels = c("counterfactual" = "Causal", "similarity" = "Similar")) +
  theme_cowplot() +
  scale_fill_manual(values = c("grey80", "#000000")) + 
  theme(axis.text.x = element_text(size = 25),
        axis.text.y = element_text(size = 25),
        axis.title.x = element_text(size = 25),
        axis.title.y = element_blank(),
        legend.text = element_text(size = 25),
        legend.title = element_text(size = 25),
        
        panel.background = element_rect(fill='transparent', color=NA),
        plot.background = element_rect(fill='transparent', color=NA),
        # panel.grid.major = element_blank(),
        # panel.grid.minor = element_blank(),
        legend.background = element_rect(fill='transparent', color = NA),
        legend.box.background = element_rect(fill='transparent', color = NA),
        legend.position = "top",
        legend.justification = "center",
        legend.key.size = unit(1, "cm"),
        legend.spacing.x = unit(1, "cm")
        ) +
  ylim(0, 100)

main_fig

main_fig <- ggsave("spp_study3.png", width = 5, height = 5, plot = main_fig, bg = "transparent")

4.2.3 plot, facet by target items

first prune text labels

dat_plot_long <- dat_plot %>%
  pivot_longer(cols = c("causal_itemA", "similar_itemA"),
               names_to = "item_type",
               values_to = "item") %>%
  group_by(subject_id, itemB) %>%
  slice(-c(2, 3))

label_data <- dat_plot_long %>%
  ungroup() %>% 
  distinct(itemB, counterfactual_type, item)

dat_plot_long %>%
  ggplot(aes(x = counterfactual_type, y = likelihood, color = counterfactual_type)) +
  geom_violin() +
  geom_jitter(width = .05, alpha = .1) +
  stat_summary(fun = mean, geom = "point", size = 4, color = "red") +
  stat_summary(fun.data = mean_se, geom = "errorbar", width = .2) +
  geom_hline(yintercept = 50, linetype = "dashed") +
  geom_text(data = label_data, aes(label = item), y = 95, vjust = 1, size = 3.5) +
  labs(y = "Likelihood of Occurring", x = "Counterfactual type") +
  scale_x_discrete(labels = c("counterfactual" = "Causal", "similarity" = "Similar")) +
  theme_bw() +
  theme(
    axis.text.x = element_text(size = 12),
    axis.text.y = element_text(size = 12),
    axis.title.x = element_text(size = 12),
    axis.title.y = element_text(size = 12),
    legend.position = "none") +
  facet_wrap(~itemB)

4.2.4 plot single subject

dat_plot_long %>% 
  filter(subject_id == "subj_01") %>% 
  ggplot(aes(x = counterfactual_type, y = likelihood, color = counterfactual_type)) +
  geom_point() +
  geom_hline(yintercept = 50, linetype = "dashed") +
  geom_text(aes(label = item), y = 95, vjust = 1, size = 3.5) +
  labs(y = "Likelihood of Occurring", x = "Counterfactual type") +
  theme_bw() +
  theme(
        axis.text.x = element_text(size = 12),
        axis.text.y = element_text(size = 12),
        axis.title.x = element_text(size = 12),
        axis.title.y = element_text(size = 12),
        legend.position = "none") +
  facet_wrap(~itemB)

5 Modelling

5.1 Effect of preceding item type

dat_model <- dat_plot %>% 
  mutate(target_likelihood = likelihood) %>% 
  mutate(preceding_item_type = factor(counterfactual_type, levels = c("similar", "causal")), 
         subject_id = as_factor(subject_id),
         causal_itemA = as_factor(causal_itemA),
         similar_itemA = as_factor(similar_itemA)) %>% 
  select(-c("likelihood", "counterfactual_type")) 

#model
model_effect_of_preceding <- lmerTest::lmer(target_likelihood ~ preceding_item_type +
                                              (1|subject_id), data = dat_model)
summary(model_effect_of_preceding)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: target_likelihood ~ preceding_item_type + (1 | subject_id)
##    Data: dat_model
## 
## REML criterion at convergence: 13703.8
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.45444 -0.84535 -0.05665  0.80415  2.91324 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_id (Intercept)  68.28    8.263  
##  Residual               765.24   27.663  
## Number of obs: 1440, groups:  subject_id, 48
## 
## Fixed effects:
##                           Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)                 54.885      1.577   75.852   34.81   <2e-16 ***
## preceding_item_typecausal  -19.317      1.458 1391.000  -13.25   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## prcdng_tm_t -0.462
plot(allEffects(model_effect_of_preceding))

#check_model(model_effect_of_condition) #binned residual issue?

#probabilities
effects_data <- allEffects(model_effect_of_preceding)
effects_df <- as.data.frame(effects_data$preceding)
effects_df
##   preceding_item_type      fit       se    lower    upper
## 1             similar 54.88472 1.576511 51.79221 57.97723
## 2              causal 35.56806 1.576511 32.47555 38.66056

5.2 Check model

check_model(model_effect_of_preceding)

5.3 Power analysis with simr

5.3.1 intercept

# First, let's check the model structure and parameter names
summary(model_effect_of_preceding)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: target_likelihood ~ preceding_item_type + (1 | subject_id)
##    Data: dat_model
## 
## REML criterion at convergence: 13703.8
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.45444 -0.84535 -0.05665  0.80415  2.91324 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_id (Intercept)  68.28    8.263  
##  Residual               765.24   27.663  
## Number of obs: 1440, groups:  subject_id, 48
## 
## Fixed effects:
##                           Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)                 54.885      1.577   75.852   34.81   <2e-16 ***
## preceding_item_typecausal  -19.317      1.458 1391.000  -13.25   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## prcdng_tm_t -0.462
fixef(model_effect_of_preceding)  # Check the actual parameter names
##               (Intercept) preceding_item_typecausal 
##                  54.88472                 -19.31667
# Extend the model for power analysis
model_simulate <- extend(model_effect_of_preceding, along = "subject_id", n = 200)

# Verify the extended model
length(unique(simr::getData(model_simulate)$subject_id)) #confirm that N is now 200
## [1] 200
# Check the parameter name in the extended model
names(fixef(model_simulate))
## [1] "(Intercept)"               "preceding_item_typecausal"
# Alternative approach: Use a different test statistic
# Sometimes the t-test doesn't work well with mixed models
# Try using the z-test instead:
curve_intercept_t <- powerCurve(model_simulate, 
                                  fixed("(Intercept)", "t"), 
                                  along = "subject_id", 
                                  breaks = c(2, 3, 4, 5, 10, 20, 30, 40, 50, 
                                             60, 70, 80, 90, 100, 
                                             110, 120, 130, 140, 150,
                                            160, 170, 180, 190, 200),
                                  nsim = 100,
                                progress = FALSE)

plot(curve_intercept_t)

print(curve_intercept_t)
## Power for predictor '(Intercept)', (95% confidence interval),
## by number of levels in subject_id:
##       2: 73.00% (63.20, 81.39) - 60 rows
##       3: 99.00% (94.55, 99.97) - 90 rows
##       4: 100.0% (96.38, 100.0) - 120 rows
##       5: 100.0% (96.38, 100.0) - 150 rows
##      10: 100.0% (96.38, 100.0) - 300 rows
##      20: 100.0% (96.38, 100.0) - 600 rows
##      30: 100.0% (96.38, 100.0) - 900 rows
##      40: 100.0% (96.38, 100.0) - 1200 rows
##      50: 100.0% (96.38, 100.0) - 1500 rows
##      60: 100.0% (96.38, 100.0) - 1800 rows
##      70: 100.0% (96.38, 100.0) - 2100 rows
##      80: 100.0% (96.38, 100.0) - 2400 rows
##      90: 100.0% (96.38, 100.0) - 2700 rows
##     100: 100.0% (96.38, 100.0) - 3000 rows
##     110: 100.0% (96.38, 100.0) - 3300 rows
##     120: 100.0% (96.38, 100.0) - 3600 rows
##     130: 100.0% (96.38, 100.0) - 3900 rows
##     140: 100.0% (96.38, 100.0) - 4200 rows
##     150: 100.0% (96.38, 100.0) - 4500 rows
##     160: 100.0% (96.38, 100.0) - 4800 rows
##     170: 100.0% (96.38, 100.0) - 5100 rows
##     180: 100.0% (96.38, 100.0) - 5400 rows
##     190: 100.0% (96.38, 100.0) - 5700 rows
##     200: 100.0% (96.38, 100.0) - 6000 rows
## 
## Time elapsed: 0 h 2 m 21 s

5.3.2 fixed effect

# First, let's check the model structure and parameter names
summary(model_effect_of_preceding)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: target_likelihood ~ preceding_item_type + (1 | subject_id)
##    Data: dat_model
## 
## REML criterion at convergence: 13703.8
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.45444 -0.84535 -0.05665  0.80415  2.91324 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_id (Intercept)  68.28    8.263  
##  Residual               765.24   27.663  
## Number of obs: 1440, groups:  subject_id, 48
## 
## Fixed effects:
##                           Estimate Std. Error       df t value Pr(>|t|)    
## (Intercept)                 54.885      1.577   75.852   34.81   <2e-16 ***
## preceding_item_typecausal  -19.317      1.458 1391.000  -13.25   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr)
## prcdng_tm_t -0.462
fixef(model_effect_of_preceding)  # Check the actual parameter names
##               (Intercept) preceding_item_typecausal 
##                  54.88472                 -19.31667
# Extend the model for power analysis
model_simulate <- extend(model_effect_of_preceding, along = "subject_id", n = 200)

# Verify the extended model
length(unique(simr::getData(model_simulate)$subject_id)) #confirm that N is now 200
## [1] 200
# Check the parameter name in the extended model
names(fixef(model_simulate))
## [1] "(Intercept)"               "preceding_item_typecausal"
# Alternative approach: Use a different test statistic
# Sometimes the t-test doesn't work well with mixed models
# Try using the z-test instead:
curve_cond_effect_t <- powerCurve(model_simulate,
                                  fixed("preceding_item_typecausal", "t"),
                                  along = "subject_id",
                                  breaks = c(2, 3, 4, 5, 10, 20, 30, 40, 50,
                                             60, 70, 80, 90, 100,
                                             110, 120, 130, 140, 150,
                                            160, 170, 180, 190, 200),
                                  nsim = 100)
## Calculating power at 24 sample sizes along subject_id
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## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |======                                                    |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |=======                                                   |( 1/24) Simulating: |========                                                  |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |=========                                                 |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |==========                                                |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |===========                                               |( 1/24) Simulating: |============                                              |( 1/24) Simulating: |=============                                             |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |==============                                            |( 1/24) Simulating: |===============                                           |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |================                                          |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |=================                                         |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |==================                                        |( 1/24) Simulating: |===================                                       |( 1/24) Simulating: |====================                                      |
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |=====================                                     |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |======================                                    |( 1/24) Simulating: |=======================                                   |( 1/24) Simulating: |========================                                  |( 1/24) Simulating: |=========================                                 |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |==========================                                |( 1/24) Simulating: |===========================                               |
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |============================                              |( 1/24) Simulating: |=============================                             |
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |==============================                            |( 1/24) Simulating: |===============================                           |
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |================================                          |( 1/24) Simulating: |=================================                         |
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |==================================                        |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |===================================                       |
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |====================================                      |( 1/24) Simulating: |=====================================                     |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |======================================                    |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |=======================================                   |( 1/24) Simulating: |========================================                  |( 1/24) Simulating: |=========================================                 |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |==========================================                |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |===========================================               |( 1/24) Simulating: |============================================              |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |=============================================             |( 1/24) Simulating: |==============================================            |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |===============================================           |( 1/24) Simulating: |================================================          |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |=================================================         |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |==================================================        |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |===================================================       |( 1/24) Simulating: |====================================================      |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |=====================================================     |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |======================================================    |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |=======================================================   |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |========================================================  |( 1/24) Simulating: |========================================================= |
## boundary (singular) fit: see help('isSingular')
## ( 1/24) Simulating: |==========================================================|( 1/24) ( 2/24) ( 2/24) Simulating: |                                                          |( 2/24) Simulating: |=                                                         |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |==                                                        |( 2/24) Simulating: |===                                                       |( 2/24) Simulating: |====                                                      |( 2/24) Simulating: |=====                                                     |( 2/24) Simulating: |======                                                    |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |=======                                                   |( 2/24) Simulating: |========                                                  |( 2/24) Simulating: |=========                                                 |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |==========                                                |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |===========                                               |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |============                                              |( 2/24) Simulating: |=============                                             |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |==============                                            |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |===============                                           |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |================                                          |( 2/24) Simulating: |=================                                         |( 2/24) Simulating: |==================                                        |( 2/24) Simulating: |===================                                       |( 2/24) Simulating: |====================                                      |
## boundary (singular) fit: see help('isSingular')
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |=====================                                     |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |======================                                    |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |=======================                                   |( 2/24) Simulating: |========================                                  |( 2/24) Simulating: |=========================                                 |( 2/24) Simulating: |==========================                                |( 2/24) Simulating: |===========================                               |( 2/24) Simulating: |============================                              |( 2/24) Simulating: |=============================                             |( 2/24) Simulating: |==============================                            |( 2/24) Simulating: |===============================                           |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |================================                          |( 2/24) Simulating: |=================================                         |( 2/24) Simulating: |==================================                        |( 2/24) Simulating: |===================================                       |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |====================================                      |( 2/24) Simulating: |=====================================                     |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |======================================                    |( 2/24) Simulating: |=======================================                   |( 2/24) Simulating: |========================================                  |( 2/24) Simulating: |=========================================                 |( 2/24) Simulating: |==========================================                |( 2/24) Simulating: |===========================================               |( 2/24) Simulating: |============================================              |( 2/24) Simulating: |=============================================             |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |==============================================            |( 2/24) Simulating: |===============================================           |( 2/24) Simulating: |================================================          |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |=================================================         |( 2/24) Simulating: |==================================================        |( 2/24) Simulating: |===================================================       |( 2/24) Simulating: |====================================================      |( 2/24) Simulating: |=====================================================     |( 2/24) Simulating: |======================================================    |( 2/24) Simulating: |=======================================================   |
## boundary (singular) fit: see help('isSingular')
## ( 2/24) Simulating: |========================================================  |( 2/24) Simulating: |========================================================= |( 2/24) Simulating: |==========================================================|( 2/24) ( 3/24) ( 3/24) Simulating: |                                                          |( 3/24) Simulating: |=                                                         |
## boundary (singular) fit: see help('isSingular')
## ( 3/24) Simulating: |==                                                        |( 3/24) Simulating: |===                                                       |( 3/24) Simulating: |====                                                      |( 3/24) Simulating: |=====                                                     |( 3/24) Simulating: |======                                                    |
## boundary (singular) fit: see help('isSingular')
## ( 3/24) Simulating: |=======                                                   |( 3/24) Simulating: |========                                                  |
## boundary (singular) fit: see help('isSingular')
## ( 3/24) Simulating: |=========                                                 |( 3/24) Simulating: |==========                                                |( 3/24) Simulating: |===========                                               |
## boundary (singular) fit: see help('isSingular')
## ( 3/24) Simulating: |============                                              |( 3/24) Simulating: |=============                                             |
## boundary (singular) fit: see help('isSingular')
## ( 3/24) Simulating: |==============                                            |
## boundary (singular) fit: see help('isSingular')
## ( 3/24) Simulating: |===============                                           |
## boundary (singular) fit: see help('isSingular')
## ( 3/24) Simulating: |================                                          |( 3/24) Simulating: |=================                                         |( 3/24) Simulating: |==================                                        |( 3/24) Simulating: |===================                                       |( 3/24) Simulating: |====================                                      |
## boundary (singular) fit: see help('isSingular')
## ( 3/24) Simulating: |=====================                                     |( 3/24) Simulating: |======================                                    |
## boundary (singular) fit: see help('isSingular')
## ( 3/24) Simulating: |=======================                                   |( 3/24) Simulating: |========================                                  |( 3/24) Simulating: |=========================                                 |( 3/24) Simulating: |==========================                                |( 3/24) Simulating: |===========================                               |( 3/24) Simulating: |============================                              |( 3/24) Simulating: |=============================                             |( 3/24) Simulating: |==============================                            |
## boundary (singular) fit: see help('isSingular')
## ( 3/24) Simulating: |===============================                           |( 3/24) Simulating: |================================                          |( 3/24) Simulating: |=================================                         |
## boundary (singular) fit: see help('isSingular')
## ( 3/24) Simulating: |==================================                        |( 3/24) Simulating: |===================================                       |( 3/24) Simulating: |====================================                      |( 3/24) Simulating: |=====================================                     |
## boundary (singular) fit: see help('isSingular')
## ( 3/24) Simulating: |======================================                    |( 3/24) Simulating: |=======================================                   |( 3/24) Simulating: |========================================                  |( 3/24) Simulating: |=========================================                 |( 3/24) Simulating: |==========================================                |( 3/24) Simulating: |===========================================               |( 3/24) Simulating: |============================================              |( 3/24) Simulating: |=============================================             |
## boundary (singular) fit: see help('isSingular')
## ( 3/24) Simulating: |==============================================            |( 3/24) Simulating: |===============================================           |( 3/24) Simulating: |================================================          |( 3/24) Simulating: |=================================================         |( 3/24) Simulating: |==================================================        |( 3/24) Simulating: |===================================================       |( 3/24) Simulating: |====================================================      |( 3/24) Simulating: |=====================================================     |( 3/24) Simulating: |======================================================    |( 3/24) Simulating: |=======================================================   |( 3/24) Simulating: |========================================================  |( 3/24) Simulating: |========================================================= |( 3/24) Simulating: |==========================================================|( 3/24) ( 4/24) ( 4/24) Simulating: |                                                          |( 4/24) Simulating: |=                                                         |( 4/24) Simulating: |==                                                        |( 4/24) Simulating: |===                                                       |( 4/24) Simulating: |====                                                      |( 4/24) Simulating: |=====                                                     |( 4/24) Simulating: |======                                                    |
## boundary (singular) fit: see help('isSingular')
## ( 4/24) Simulating: |=======                                                   |( 4/24) Simulating: |========                                                  |
## boundary (singular) fit: see help('isSingular')
## ( 4/24) Simulating: |=========                                                 |( 4/24) Simulating: |==========                                                |
## boundary (singular) fit: see help('isSingular')
## ( 4/24) Simulating: |===========                                               |( 4/24) Simulating: |============                                              |( 4/24) Simulating: |=============                                             |
## boundary (singular) fit: see help('isSingular')
## ( 4/24) Simulating: |==============                                            |( 4/24) Simulating: |===============                                           |
## boundary (singular) fit: see help('isSingular')
## ( 4/24) Simulating: |================                                          |( 4/24) Simulating: |=================                                         |( 4/24) Simulating: |==================                                        |( 4/24) Simulating: |===================                                       |( 4/24) Simulating: |====================                                      |
## boundary (singular) fit: see help('isSingular')
## ( 4/24) Simulating: |=====================                                     |( 4/24) Simulating: |======================                                    |( 4/24) Simulating: |=======================                                   |( 4/24) Simulating: |========================                                  |( 4/24) Simulating: |=========================                                 |( 4/24) Simulating: |==========================                                |( 4/24) Simulating: |===========================                               |( 4/24) Simulating: |============================                              |( 4/24) Simulating: |=============================                             |( 4/24) Simulating: |==============================                            |
## boundary (singular) fit: see help('isSingular')
## ( 4/24) Simulating: |===============================                           |( 4/24) Simulating: |================================                          |( 4/24) Simulating: |=================================                         |( 4/24) Simulating: |==================================                        |( 4/24) Simulating: |===================================                       |( 4/24) Simulating: |====================================                      |( 4/24) Simulating: |=====================================                     |
## boundary (singular) fit: see help('isSingular')
## ( 4/24) Simulating: |======================================                    |( 4/24) Simulating: |=======================================                   |( 4/24) Simulating: |========================================                  |( 4/24) Simulating: |=========================================                 |( 4/24) Simulating: |==========================================                |( 4/24) Simulating: |===========================================               |( 4/24) Simulating: |============================================              |( 4/24) Simulating: |=============================================             |
## boundary (singular) fit: see help('isSingular')
## ( 4/24) Simulating: |==============================================            |( 4/24) Simulating: |===============================================           |( 4/24) Simulating: |================================================          |( 4/24) Simulating: |=================================================         |( 4/24) Simulating: |==================================================        |( 4/24) Simulating: |===================================================       |( 4/24) Simulating: |====================================================      |( 4/24) Simulating: |=====================================================     |( 4/24) Simulating: |======================================================    |( 4/24) Simulating: |=======================================================   |( 4/24) Simulating: |========================================================  |( 4/24) Simulating: |========================================================= |( 4/24) Simulating: |==========================================================|( 4/24) ( 5/24) ( 5/24) Simulating: |                                                          |( 5/24) Simulating: |=                                                         |( 5/24) Simulating: |==                                                        |( 5/24) Simulating: |===                                                       |( 5/24) Simulating: |====                                                      |( 5/24) Simulating: |=====                                                     |( 5/24) Simulating: |======                                                    |( 5/24) Simulating: |=======                                                   |( 5/24) Simulating: |========                                                  |( 5/24) Simulating: |=========                                                 |( 5/24) Simulating: |==========                                                |
## boundary (singular) fit: see help('isSingular')
## ( 5/24) Simulating: |===========                                               |( 5/24) Simulating: |============                                              |( 5/24) Simulating: |=============                                             |( 5/24) Simulating: |==============                                            |( 5/24) Simulating: |===============                                           |( 5/24) Simulating: |================                                          |( 5/24) Simulating: |=================                                         |( 5/24) Simulating: |==================                                        |( 5/24) Simulating: |===================                                       |( 5/24) Simulating: |====================                                      |
## boundary (singular) fit: see help('isSingular')
## ( 5/24) Simulating: |=====================                                     |( 5/24) Simulating: |======================                                    |( 5/24) Simulating: |=======================                                   |( 5/24) Simulating: |========================                                  |( 5/24) Simulating: |=========================                                 |( 5/24) Simulating: |==========================                                |( 5/24) Simulating: |===========================                               |( 5/24) Simulating: |============================                              |( 5/24) Simulating: |=============================                             |( 5/24) Simulating: |==============================                            |( 5/24) Simulating: |===============================                           |( 5/24) Simulating: |================================                          |( 5/24) Simulating: 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|========================================================= |( 5/24) Simulating: |==========================================================|( 5/24) ( 6/24) ( 6/24) Simulating: |                                                          |( 6/24) Simulating: |=                                                         |( 6/24) Simulating: |==                                                        |( 6/24) Simulating: |===                                                       |( 6/24) Simulating: |====                                                      |( 6/24) Simulating: |=====                                                     |( 6/24) Simulating: |======                                                    |( 6/24) Simulating: |=======                                                   |( 6/24) Simulating: |========                                                  |( 6/24) Simulating: |=========                                                 |( 6/24) Simulating: |==========              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## Warning in observedPowerWarning(sim): This appears to be an "observed power"
## calculation
plot(curve_cond_effect_t)

print(curve_cond_effect_t)
## Power for predictor 'preceding_item_typecausal', (95% confidence interval),
## by number of levels in subject_id:
##       2: 74.00% (64.27, 82.26) - 60 rows
##       3: 89.00% (81.17, 94.38) - 90 rows
##       4: 96.00% (90.07, 98.90) - 120 rows
##       5: 100.0% (96.38, 100.0) - 150 rows
##      10: 100.0% (96.38, 100.0) - 300 rows
##      20: 100.0% (96.38, 100.0) - 600 rows
##      30: 100.0% (96.38, 100.0) - 900 rows
##      40: 100.0% (96.38, 100.0) - 1200 rows
##      50: 100.0% (96.38, 100.0) - 1500 rows
##      60: 100.0% (96.38, 100.0) - 1800 rows
##      70: 100.0% (96.38, 100.0) - 2100 rows
##      80: 100.0% (96.38, 100.0) - 2400 rows
##      90: 100.0% (96.38, 100.0) - 2700 rows
##     100: 100.0% (96.38, 100.0) - 3000 rows
##     110: 100.0% (96.38, 100.0) - 3300 rows
##     120: 100.0% (96.38, 100.0) - 3600 rows
##     130: 100.0% (96.38, 100.0) - 3900 rows
##     140: 100.0% (96.38, 100.0) - 4200 rows
##     150: 100.0% (96.38, 100.0) - 4500 rows
##     160: 100.0% (96.38, 100.0) - 4800 rows
##     170: 100.0% (96.38, 100.0) - 5100 rows
##     180: 100.0% (96.38, 100.0) - 5400 rows
##     190: 100.0% (96.38, 100.0) - 5700 rows
##     200: 100.0% (96.38, 100.0) - 6000 rows
## 
## Time elapsed: 0 h 2 m 23 s

5.4 plot dv vs distances

5.4.1 prepare append distances

distances <- read_csv(freesort_and_causal_distances_df_path)
## Rows: 210 Columns: 7
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (4): itemA, itemB, domain_itemA, domain_itemB
## dbl (3): mean_causal_distance, mean_freesort_distance, freesort_minus_causal
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
dat_distances <- dat_plot_long %>% 
  ungroup() %>% 
  rename("itemA" = item) %>% 
  left_join(distances %>% 
              select(itemB, itemA, mean_causal_distance, mean_freesort_distance, freesort_minus_causal),
            by = c("itemB", "itemA")) %>% 
  mutate(mean_causal_distance = round(mean_causal_distance, 2),
         mean_freesort_distance = round(mean_freesort_distance, 2),
         freesort_minus_causal = round(freesort_minus_causal, 2)) %>% 
  mutate(itemB = factor(itemB, levels = desired_order))

5.4.2 plot difference scores

15 similar item - target item pairs, 15 causal item - target item pairs. The more causal (right of x -axis), the less likely the counterfactual event will occur

#make separate data frame with only distances and difference scores?
#or, get the mean responses and an error bar for it?

#parcel out labels
label_distances <- dat_distances %>%
  distinct(itemB, counterfactual_type, itemA, freesort_minus_causal)
    

#plot
dat_distances %>% 
  ggplot(aes(x = freesort_minus_causal, y = likelihood, color = counterfactual_type)) +
  geom_point(alpha = .2) +
  geom_text(data = label_distances, aes(label = itemB), y = 95, vjust = .5, size = 3.5, angle = 80) +
  geom_text(data = label_distances, aes(label = itemA), y = 85, vjust = .5, size = 3.5, angle = 80) +
  stat_summary(fun.data = mean_se, geom = "errorbar", width = .01, color = "black") +
  stat_summary(fun = "mean", geom = "point", shape = 1, size = 3, color = "black") +
  geom_smooth(method = "lm") +
  geom_hline(yintercept = 50, linetype = "dashed") +
  theme_bw() +
  labs(y = "Likelihood of Occurring", x = "Freesort minus Causal Distance") +
  theme_bw() +
  theme(
        axis.text.x = element_text(size = 12),
        axis.text.y = element_text(size = 12),
        axis.title.x = element_text(size = 12),
        axis.title.y = element_text(size = 12))
## `geom_smooth()` using formula = 'y ~ x'

5.4.3 itemwise difference scores

dat_distances %>% 
  ggplot(aes(x = freesort_minus_causal, y = likelihood, color = counterfactual_type)) +
  geom_point(alpha = .2) +
  geom_text(data = label_distances, aes(label = itemA), y = 90, size = 3.5) +
  stat_summary(fun.data = mean_se, geom = "errorbar", width = .03, color = "black") +
  stat_summary(fun = "mean", geom = "point", shape = 1, size = 2, color = "black") +
  geom_smooth(method = "lm") +
  geom_hline(yintercept = 50, linetype = "dashed") +
  theme_bw() +
  labs(y = "Likelihood of Occurring", x = "Freesort minus Causal Distance") +
  theme_bw() +
  theme(
        axis.text.x = element_text(size = 12),
        axis.text.y = element_text(size = 12),
        axis.title.x = element_text(size = 12),
        axis.title.y = element_text(size = 12)) +
  facet_wrap(~itemB)
## `geom_smooth()` using formula = 'y ~ x'

5.4.4 plot individual distances

dat_distances %>% 
  pivot_longer(cols = c("mean_causal_distance", "mean_freesort_distance"),
               names_to = "distance_type", 
               values_to = "distances") %>% 
  ggplot(aes(x = distances, y = likelihood, color = distance_type)) +
  geom_jitter(width = .01, alpha = .2) +
  geom_smooth(method = "lm") +
  geom_hline(yintercept = 50, linetype = "dashed") +
  theme_bw() +
  labs(y = "Likelihood of Occurring", x = "Distance") +
  theme_bw() +
  theme(
        axis.text.x = element_text(size = 12),
        axis.text.y = element_text(size = 12),
        axis.title.x = element_text(size = 12),
        axis.title.y = element_text(size = 12)) +
  facet_wrap(~item_type)
## `geom_smooth()` using formula = 'y ~ x'